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B
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Difficulty:
65%
(hard)
Question Stats:
57% (02:31) correct
43%
(02:51)
wrong
based on 367
sessions
History
Date
Time
Result
Not Attempted Yet
Is 3^(p-2) greater than 1,000?
(1) 3^(p+1)< 54,000
(2) 3^p < 3^(p-1) + 2,000
(1) 3^(p+1)< 54,000
(2) 3^p < 3^(p-1) + 2,000
14 Jan 2014, 01:37
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Is 3^(p-2) greater than 1,000?
(1) 3^(p+1)< 54,000 --> \(3^{p+1}< 27*2,000\) --> \(3^{p+1}< 3^3*2,000\) --> divided both sides by 3^3: \(3^{p-2}< 2,000\). Thus 3^(p-2) may or may not be greater than 1,000. Not sufficient.
(2) 3^p < 3^(p-1) + 2,000 --> \(3^p -3^{p-1}< 2,000\) --> factor out 3^(p-2): \(3^{p-2}(3^2 -3)< 2,000\) --> \(3^{p-2}< \frac{1,000}{3}\). Sufficient.
Answer: B.
(1) 3^(p+1)< 54,000 --> \(3^{p+1}< 27*2,000\) --> \(3^{p+1}< 3^3*2,000\) --> divided both sides by 3^3: \(3^{p-2}< 2,000\). Thus 3^(p-2) may or may not be greater than 1,000. Not sufficient.
(2) 3^p < 3^(p-1) + 2,000 --> \(3^p -3^{p-1}< 2,000\) --> factor out 3^(p-2): \(3^{p-2}(3^2 -3)< 2,000\) --> \(3^{p-2}< \frac{1,000}{3}\). Sufficient.
Answer: B.
14 Jan 2014, 01:39
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Bunuel
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Hope this helps.
